Zevachim 16 - Who Cannot Do Sacrificial Service
The following categories of people, if they receive the blood of the sacrifice, invalidate the offering:
A non-Kohen. Only the priests who are the descendants of Aharon can serve in the Temple. The Torah said, " Speak to Aaron and to his sons that they shall separate themselves from the holies of the children of Israel and they shall not profane ..."
A kohen whose relative, one of the seven close ones - father, mother, brother, unmarried sister, son, daughter, or spouse - has died this day. Since Aharon was specifically requested to continue the service after his two sons died, " And he need not leave the Sanctuary and he will not profane ...", we understand that all other Kohanim would profane the service.
Although the ruling above mentions only receiving the blood, the same disqualification also applies to the other two steps - carrying the blood and throwing it on the Altar. The slaughter, however, is valid if done by a non-Kohen, since the Torah said, "And he slaughters, and a Kohen receives the blood."
Art: Pierre Auguste Renoir - The Artists Family